Content

• To step
• Method 1 of 2: Simple equations with 2 variables
• Method 2 of 2: For quadratic equations
• Tips

In algebra, 2-dimensional graphs with coordinates have a horizontal axis, or x-axis, and a vertical axis, or y-axis. The places where lines representing a series of values ​​intersect these axes are called intersection points. The y intercept is where the line intersects the y axis, and the x intercept is where the line intersects the x axis. Finding the x-intersection with algebra can be simple or complex, depending on whether the equation has only 2 variables or is quadratic. The steps below show how it works for both types of equations.

To step

Method 1 of 2: Simple equations with 2 variables

1. Replace the value of y with 0. At the point where the value line crosses the horizontal axis, y has a value of 0.
   • If you replace 2x + 3y = 6, y with 0 in the example equation, the equation changes to 2x + 3 (0) = 6, so basically just 2x = 6.
2. Find the solution for x. This usually means dividing both sides of the equation by the coefficient for x to give it a value of 1.
   • In the example equation above, if you divide both sides by 2, 2x = 6, you get 2/2 x = 6/2, or x = 3. This is the x intersection for the equation 2x + 3y = 6.
   • You can use the same steps for equations of the form ax ^ 2 + by ^ 2 = c. In this case, if you put 0 for y, you get x ^ 2 = c / a, and after you find the value to the right of the equal sign, you need to find the square root of x squared. This gives you 2 values, 1 positive and 1 negative, which add up to 0.

Method 2 of 2: For quadratic equations

1. Put the equation in the form ax ^ 2 + bx + c = 0. This is the standard form for writing a quadratic equation, where a represents the coefficient for x-squared, b the coefficient for x, and c is a purely numerical value.
   • For the example in this section, we'll use the equation x ^ 2 + 3x - 10 = 0.
2. Solve the equation for x. There are several ways to solve a quadratic equation. The 2 we will discuss here are factoring and using the quadratic formula.
   • In factoring, you split a quadratic equation into 2 simpler algebraic expressions that, when multiplied together, produce the quadratic equation. Often times the values ​​of a and c can be the key to finding the correct factors. Since 2 times 5 equals 10, the absolute value of c, and because the absolute value of b is less than that of c, 2 and 5 are likely the numerical components of the correct factors. Since 5 minus 2 equals 3, the correct factors are x + 5 and x - 2. If you enter the factors for the quadratic equation, (x + 5) (x - 2) = 0, the 2 x intersection points are -5 (-5 + 5 = 0) and 2 (2 - 2 = 0).
   • Using the quadratic formula, enter the values ​​for a, b, and c from the quadratic formula into the formula (-b + or - W (b ^ 2 - 4 ac)) / 2a (where W is the square root ) to find the value or values ​​for x.
   • If you put the values ​​1, 3, and -10 in this equation, you get (-3 + or - W (3 ^ 2 - 4 (1) (- 10))) / 2 (1). The value inside the W brackets comes out to 9 - (- 40) which is 9 + 40, which is 49, so the equation comes out to (-3 + or - 7) / 2, which gives (-3 + 7 ) / 2 or 4/2, which is 2, and (-3 -7) / 2 or -10/2, which is -5.
   • Unlike the simple 2-variable equations described in the previous section, quadratic equations on a coordinate graph are drawn as a parabola (a curve that resembles a "U" or "V") instead of a straight line. . Quadratic equations cannot have an x ​​intersection, 1 x intersection, or 2 x intersections.

Tips

• If you enter a 0 for x instead of y in the example equation under "Simple equations with 2 variables", you can find out the value of the y intercept.